Termination with extreme prejudice refers to is supposed to refer only to the assasination of one's own employee. Generally used in espionage circles, although it's certainly possible for any particularly unethical employer to apply it.

It's meant to be a bit of a pun on the phrase "termination with prejudice," with the "termination" in this case referring both to the end of the employee's employment with that particular employer, as well as to the end of their life. In espionage and military circles, though, it is never used to describe killing a foreign agent.